theorem
  (e1,e2) interval_in (p,tr) c= (e1,e2) inter
proof
  let o be object such that O1: o in (e1,e2) interval_in (p,tr);
  consider e such that O2: e = o & e1 < e & e < e2 & e in p,tr by O1;
  thus thesis by O2;
end;
